Qubit-efficient quantum combinatorial-optimization solver

Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient algorithm that overcomes this limitation by mapping a candidate bit string solution to an entangled wave function of fewer qubits. We propose a variational quantum circuit generalizing the quantum approximate optimization ansatz (QAOA). Extremizing the ansatz for Sherrington-Kirkpatrick spin glass problems, we show valuable properties such as the concentration of ansatz parameters and derive performance guarantees. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.